Calculations using Orgel diagrams
Orgel diagrams are useful for showing the energy levels of bothhigh spin octahedral and tetrahedral transition metal ions. TheyONLY show the spin-allowed transitions.For complexes with D ground terms only one electronic transitionis expected and the transition energy corresponds directly toΔ. Hence, the following high spinconfigurations are dealt with: d1, d4,d6 and d9.
D Orgel diagram
On the left hand side d1, d6 tetrahedraland d4, d9 octahedral complexes are coveredand on the right hand side d4, d9tetrahedral and d1, d6 octahedral.
For simplicity, the g subscripts required for the octahedralcomplexes are not shown.
For complexes with F ground terms, three electronic transitionsare expected and Δ may not corresponddirectly to a transition energy. The following configurations aredealt with: d2, d3, high spin d7and d8.
F Orgel diagram
On the left hand side, d2, d7 tetrahedraland d3, d8 octahedral complexes are coveredand on the right hand side d3, d8tetrahedral and d2 and high spin d7octahedral.
Again for simplicity, the g subscripts required for theoctahedral complexes are not shown.
On the left hand side, the first transition corresponds to Δ, the equation to calculate the secondcontains expressions with both Δ and C.I.(the configuration interaction from repulsion of like terms) andthe third has expressions which contain Δ, C.I. and the Racah parameter B.
- 4T2g ← 4A2g transition energy = Δ
- 4T1g(F) ← 4A2g transition energy = 9/5 * Δ - C.I.
- 4T1g(P) ← 4A2g transition energy = 6/5 * Δ + 15B' + C.I.
On the right hand side,
The first transition can be unambiguously assigned as:
3T2g ← 3T1gtransition energy = 4/5 * Δ + C.I.But, depending on the size of the ligand field (Δ) the second transition may be due to:
3A2g ← 3T1g transition energy = 9/5 *Δ + C.I.for a weak field or
3T1g(P) ← 3T1gtransition energy = 3/5 * Δ + 15B' + 2 * C.I.for a strong field.
TANABE-SUGANO DIAGRAMS
An alternative method is to use Tanabe Sugano diagrams, which areable to predict the transition energies for both spin-allowed andspin-forbidden transitions, as well as for both strong field (lowspin), and weak field (high spin) complexes.Note however that most textbooks only give Tanabe-Sugano diagramsfor octahedral complexes and a separate diagram is required foreach configuration.
In this method the energy of the electronic states are given onthe vertical axis and the ligand field strength increases on thehorizontal axis from left to right.
Linear lines are found when there are no other terms of the sametype and curved lines are found when 2 or more terms arerepeated. This is as a result of the "non-crossing rule".
The baseline in the Tanabe-Sugano diagram represents the lowestenergy or ground term state.
The d2 case (not many examplesdocumented).
The electronic spectrum of the V3+ ion, where V(III)is doped into alumina (Al2O3), shows threemajor peaks with frequencies of: ν1=17400cm-1, ν2=25400 cm-1and ν3=34500 cm-1.
These have been assigned to the followingspin-allowed transitions.
| 3T2g | <--- | 3T1g |
| 3T1g(P) | <--- | 3T1g |
| 3A2g | <--- | 3T1g |
The ratio between the first two transitions is calculated asν2 / ν1 which is equal to 25400 / 17400 = 1.448.
In order to calculate the Racah parameter, B,the position on the horizontal axis where the ratio between thelines representing ν2 and ν1 is equal to 1.448, has to be determined. Onthe diagram below, this occurs at Δ/B=30.9. Having found this value, a vertical line is drawn at this position.
Tanabe-Sugano diagram for d2 octahedral complexes
On moving up the line from the ground term to where lines fromthe other terms cross it, we are able to identify both thespin-forbidden and spin-allowed transition and hence the totalnumber of transitions that are possible in the electronicspectrum.
Next, find the values on the vertical axis that correspond to thespin-allowed transitions so as to determine the values of ν1/B, ν2/B and ν3/B. From the diagram above these are 28.78, 41.67 and 59.68 respectively.
Knowing the values of ν1, ν2 and ν3, we can nowcalculate the value of B.
Since ν1/B=28.78 and ν1 is equal to 17,400 cm-1, thenB=ν1/28.78 = 17400/28.78
or B=604.5cm-1
Then it is possible to calculate the value of Δ.
Since Δ/B=30.9, then: Δ=B*30.9 and hence: Δ =604.5 * 30.9 = 18680 cm-1
Calculate the value of B and Δ for the Cr3+ ion in[Cr(H2O)6)]3+ if ν1=17000 cm-1, ν2=24000 cm-1 and ν3=37000 cm-1.
SOLUTION.
These values have been assigned to the followingspin-allowed transitions.
| 4T2g | <--- | 4A2g |
| 4T1g | <--- | 4A2g |
| 4T1g(P) | <--- | 4A2g |
Using a Tanabe-Sugano diagram for a d3 system this ratio is foundat Δ/B=24.00
Tanabe-Sugano diagram for d3 octahedral complexes
ν1/B=24.00Recall that ν1=17000 cm-1.Therefore for the first spin-allowed transition,
ν2/B=33.90
ν3/B=53.11
17000 /B =24.00 from which B can be obtained, B=17000 / 24.00 orB=708.3 cm-1.
This information is then used to calculate Δ.
Since Δ / B=24.00 then Δ = B*24.00 = 708.3 * 24.00 = 17000cm-1.
It is observed that the value of Racah parameter B in thecomplex is 708.3 cm-1, while the value of B in thefree Cr3+ ion is 1030cm-1. This shows a 31%reduction in the Racah parameter indicating a strongNephelauxetic effect.
The Nephelauxetic Series is as follows:
F->H2O>urea>NH3>en~C2O42->NCS->Cl-~CN->Br->S2- ~I-.
Ionic ligands such as F-give small reduction in B,while covalently bonded ligands such as I- give alarge reduction in B.
Note
The original paper by Tanabe and Sugano[10] had the d5and d6 diagrams each missing a T term from excited Istates. These diagrams were reproduced in the often quoted textby Figgis[12(a)] and so the errors have been perpetuated. Anexception is the text by Purcell and Kotz[15] where the missing Tterms have been included, however in their case they have ignoredlower lying terms from excited D, F, G and H states which ford5 are the main transitions seen in the spin forbiddenspectra of Mn(II) complexes.A set of qualitative diagrams have beendrawn for each configuration (which include the missing T terms)and along with the newest release of "Ligand Field Theory and its applications"by Figgis and Hitchman [12(b)] represent the only examples of Tanabe-Sugano diagramsthat provide a comprehensive set of terms for spectral interpretation.
References
1. Basic Inorganic Chemistry, F.A.Cotton, G.Wilkinson andP.L.Gaus, 3rd edition, John Wiley and Sons, Inc. New York,1995.2. Physical Inorganic Chemistry, S.F.A.Kettle, Oxford UniversityPress, New York, 1998.
3. Complexes and First-Row Transition Elements, D.Nicholls,Macmillan Press Ltd, London 1971.
4. The Chemistry of the Elements, N.N.Greenwood and A.Earnshaw,Pergamon Press, Oxford, 1984.
5. Concepts and Models of Inorganic Chemistry, B.E.Douglas,D.H.McDaniel and J.J.Alexander 2nd edition, John Wiley &Sons, New York, 1983.
6. Inorganic Chemistry, J.A.Huheey, 3rd edition, Harper &Row, New York, 1983.
7. Inorganic Chemistry, G.L.Meissler and D.A.Tarr, 2nd edition,Prentice Hall, New Jersey, 1998.
8. Inorganic Chemistry, D.F.Shriver and P.W.Atkins, 3rd edition,W.H.Freeman, New York, 1999.
9. Basic Principles of Ligand Field Theory, H.L.Schlafer andG.Gliemann, Wiley-Interscience, New York, 1969.
10. Y.Tanabe and S.Sugano, J. Phys. Soc. Japan, 9, 1954, 753 and766.
11(a). Inorganic Electronic Spectroscopy, A.B.P.Lever, 2ndEdition, Elsevier Publishing Co., Amsterdam, 1984.
11(b). A.B.P.Lever in Werner Centennial, Adv. in Chem Series,62, 1967, Chapter 29, 430.
12(a). Introduction to Ligand Fields, B.N.Figgis, Wiley, New York,1966.
12(b). Ligand Field Theory and its applications, B.N. Figgis andM.A. Hitchman, Wiley-VCH, New York, 2000.
13. E.Konig, Structure and Bonding, 9, 1971, 175.
14. Y. Dou, J. Chem. Educ, 67, 1990, 134.
15. Inorganic Chemistry, K.F. Purcell and J.C. Kotz, W.B.Saunders Company, Philadelphia, USA, 1977.
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